A couple months ago I recorded a podcast with Lex Fridman, it’s now available here.
A lot of Fridman’s other interviews are well worth watching or listening to, and I thought we had an interesting conversation. I can’t stand listening to or watching myself, so not sure how it turned out. But happy to answer here any questions about what we were discussing.
During recent travels I attended two conferences (in Paris and Berkeley) and met up with quite a few people. At the Paris conference I gave an intentionally provocative talk to the philosophers of physics there, slides are here. The argument I was trying to make is essentially that more attention should be paid to evidence for a deep unity in much of modern mathematics, which at the same time is connected to our best unified theory of physics (the Standard Model and GR). Edward Frenkel has made some similar points, referring to the Langlands program and its connections to physics as a “Grand Unified Theory of Mathematics”. The specific structures underlying this unification seem to me to deserve attention as providing an important way of thinking about what’s at the “foundations” of both math and physics.
Another motivation for this talk was to make an argument against what I see as having become a widespread and standard ideology about the search for a unified theory in physics. Talking to many physicists and mathematicians interested in physics, I noticed that the conventional wisdom, shared by the establishment and contrarians alike, is that the SM and GR are likely low energy emergent theories, that some completely different sort of theory is needed to describe very short distances such as the Planck scale. Physics establishment figures tend to believe that following the path started with string theory, then AdS/CFT, lately quantum error correction or whatever, will someday lead to a dramatically different sort of theory, replacing space, time and maybe quantum mechanics. Contrarians often have their own favorite idea for a radically different starting point. For an example of this, take a look at Figures 2 and 3 of Mike Freedman’s The Universe from a Single Particle (he spoke about this in Berkeley). Figure 2 is the “establishment” picture, with AdS/CFT the fundamental theory, well-decoupled from the emergent SM + GR (since no one has any idea how to relate them). His Figure 3 shows his own proposal, even better decoupled from any connection to the SM + GR.
Given the extreme level of experimental success of the SM + GR, the obvious conjecture is that these are close to a unified theory valid at all distances. That the mathematical framework they are built on is closely connected to unifying structures in mathematics provides yet more evidence that what one is looking for is not something completely different. The odd thing about the present moment is that arguing that our well-established successful theories can provide a solid basis for further unification makes one a contrarian, with the “establishment” position that a revolution sweeping such theories aside is needed.
I hope to find time in the next few weeks to write up what’s outlined in the slides as a more detailed article of some sort. More immediately, I plan to write a blog entry and perhaps some more detailed notes about the “twistor $P^1$” mentioned at the end of the talk, explaining how it shows up in Euclidean twistor theory as well as in recent work on the Langlands program.
I haven’t been posting here for a while, partly due to a lot of traveling, partly due to some personal time-consuming commitments, and largely due to a lack of much in the way of news that seemed worth much attention. For some examples of such news that might be of interest:
- Due to discovery of a buckled RF finger, the LHC start-up (at 6.8 TeV/beam) has been delayed from end of next February to end of March or beginning of April. For details, see here.
- As usual in the US for many years, no one knows what the Federal HEP physics budget for the current fiscal year is, although we’re a couple months into it. The formal US budgeting process involves a long process including an executive branch budget proposal and congressional committee hearings and debate. This however does not lead to actual budget numbers, which only emerge at the last minute, made in some way understandable to no one I’ve ever asked about this. From the latest news, the US might have a budget any day now, and then a bit later we’ll find out what the HEP budget will be.
This year the process has involved a highly peculiar situation with the budget for US LHC contributions (prospects for large cuts, assumed to get fixed mysteriously in the last minute process). For the details of what is going on, there’s a news story here, and discussion at an HEPAP meeting here. For the first time I’m aware of, the HEPAP meeting videos are on Youtube (see links here), so one can follow the actual discussion between physicists and government officials there.
- In non-news about the abc conjecture, the Japanese media appears to be reporting uncritically about IUT-based claims of proofs that are not accepted by the vast majority of experts in the subject. There have been a couple of workshops devoted to IUT (see here and here) recently, with those speaking about IUT almost all based at RIMS. Recently Mochizuki has posted a strange Invitation to view IUT workshop videos. To view the videos you have to apply, and promise not to use them for “non-mathematical purposes”. My guess is that one of the “non-mathematical purposes” at issue would be bloggers pointing out that nowhere in the talks does anyone discuss the fact that convincing arguments have been given by Peter Scholze and Jacob Stix that the IUT-based proof of abc is flawed and cannot possibly work. This problem is addressed with:
Unfortunately, it has come to my attention that certain misunderstandings concerning IUT continue to persist in certain parts of the world. Perhaps the most famous misunderstanding concerns an asserted identification of “redundant copies”. This misunderstanding involves well-known, essentially elementary mathematics at the beginning graduate level concerning the general nonsense surrounding “gluings”. For instance, if one “applies” this misunderstanding to the well-known gluing construction of the projective line, then one concludes that the two copies of the affine line that appear in this gluing are “redundant’’, hence may be identified. This identification leads immediately to a contradiction, i.e., to a “proof” that the projective line cannot exist! More details may be found in the Introduction to [EssLgc] and the references given there.
In case anyone thinks it’s plausible that Peter Scholze is making errors in elementary mathematics at the beginning graduate level, David Roberts has an explanation of what’s going on here.
On the string theory front, it’s become impossible to figure out how to have any sort of scientific debate about most of the public defenses of “string theory”. For two recent examples:
- In an article about What We Will Never Know, David Gross rather explicitly acknowledges that prospects for testing ideas about string theory are now an issue of “faith”, with no hope of turning into science any time soon:
There’s faith that one way or another we should be able to test these ideas… It might be very indirect—but that’s not something that’s a pressing issue.
- For Nabil Iqbal, string theory is now to be understood at the pre-scientific level of parable. In his parable, human beings trying to understand the equations of string theory are like fish trying to understand the equations governing the behavior of water. I’m trying to think of a sensible comment about this, but I’ve got nothing.
First some personally relevant items:
- I finally have a finished version 2.0 of my euclidean twistor unification paper (discussed here), it’s uploaded to the arXiv, should appear there Monday.
- I’ll be giving a talk October 30th at the Foundations 2021 conference in Paris, something about the unity of math and physics, and will take the opportunity to spend about two weeks in Europe, mostly in Paris.
- In other travels, I’ll be in the Bay area for a week or so mid-November.
- For entertainment I tried out a WordPress plugin that dumps all my blog content into a single pdf. If you want 8,518 pages to read at your leisure when you’re not connected to the internet, this would be one way to spend your time.
In math and physics news, there’s:
- David Mumford has a had a remarkable career, first as an algebraic geometer (he won a Fields Medal for his work in this area) and later in the field of computer vision. He’s also known as a talented expositor, with his books and papers the standard references for several different topics. He’s moved into physics this month, with a wonderful article about cosmology in the Notices. His blog is well-worth following, it had the cosmology piece a few months back.
- Also in the Notices is a set of memorial articles about Lucien Szpiro, who passed away last year. I wrote a little bit about him here, am very pleased to see these articles which give a detailed picture of both the person and his mathematics.
- The Simons Collaboration on Global Categorical Symmetries had its kick-off meeting this week in Stony Brook, videos available here. There are many interesting talks to watch. I got very excited for a minute (around :05:00 in this video) when Greg Moore started talking about some of my favorite questions (e.g. what is the representation theory of gauge groups in dimension greater than one?). But then I realized he had labeled these “Traditional Questions”, in Fraktur font to emphasize how old and out of date they were. He described these as “old-fashioned questions”, that people were not seriously working on anymore. As he explained, you’re no longer supposed to be thinking about a fixed topology, but looking for something more general that treats all topologies. My problem with this is that one tends to get interesting results about topology this way, but the physics applications seem to be in condensed matter physics, with little relevance to questions about local fundamental physics that have always been my main interest.
- I really don’t understand the thinking in physics theses days at all. Nima Arkani-Hamed is a remarkable theorist who came up with a lot of highly speculative ideas about particle physics that have never worked out, then moved on to brilliant work leading efforts that have transformed the study of scattering amplitudes. The APS just announced that he’s getting the 2022 J. J. Sakurai Prize for Theoretical Particle Physics, for “the development of transformative new frameworks”. These “transformative new frameworks” are listed as “work on large extra dimensions, the Little Higgs, and more generally for new ideas connected to the origin of the electroweak scale”, none of which has had any success, while the amplitudes work is ignored.
The latest from the BBC:
String theory – a simple way to understand the universe
Not worth more comment than it’s another reminder that this nonsense continues to be heavily promoted in our most prominent and respected mass media. I’m beginning to doubt we’re going to be rid of it in my (or anyone’s) lifetime.
I just noticed that Gordon Kane has recently published a second edition of his 2017 String Theory and the Real World. Columbia doesn’t seem to yet have full online access to the second edition, but one can already compare the two editions in a few places. For instance, on page 1-5 of the 2017 edition one reads
The LHC is now working in a region of energy and intensity where well-motivated theories imply superpartners could be seen by late 2018.
There is good reason, based on theory, to think discovery of the superpartners of Standard Model particles should occur at the CERN LHC in the next few years.
The corresponding first chapter of the latest edition has:
The LHC has so far just entered the region of superpartner masses predicted by compactiﬁed theories, which ranges from about 1.5 to ∼5 GeV (we’ll discuss that range later). Those values are the only physics predictions, rather than just speculations. The LHC will run with higher luminosity after an upgrade, beginning in late 2021 if pandemic work stoppages do not delay it. That increases the possibility of discovery, though not very much. A higher energy collider is needed. From what we know now, a collider with twice the LHC energy range would probably sufﬁce, and cover the region of gluino masses to about 5 GeV.
The concluding chapter of the 2017 edition tell us:
The compactiﬁed M-theory implies that three superpartners (and only three) will be observed at the LHC in the current three-year run (assuming the full integrated luminosity is achieved). These are the gluino and the charged and neutral winos.
Presumably he’s talking about the LHC Run II (2015-18) which did meet its luminosity goals, without any hint of the three superpartners. I don’t yet have access to the later parts of the 2021 edition to see what they say about this.
This isn’t the first time Kane has published multiple editions of ever changing “predictions” about supersymmetry. At one point I compared the 2000 and 2013 editions of “Supersymmetry and Beyond”, you can see the results here.
First some items on the mathematics side:
- The latest AMS Notices has some memorial pieces about Vaughan Jones and Robert Hermann. I contributed a piece to the Hermann memorial, for more about him, see here.
- If you read French you might enjoy Yves André’s Dix regards sur la mathématique contemporaine, freely available here.
- There’s a wonderful overview of various conjectures in number theory last year from Barry Mazur, About Main Conjectures.
- The Harvard Math department seems to not have had a lot of luck with its funders. Last spring they had to close their Program in Evolutionary Dynamics, which was funded by Jeffrey Epstein. The very active Center of Mathematical Sciences and Applications has been funded by the Evergrande Group, a real estate investment company that has now run into serious financial problems. I haven’t heard what the implications will be for the CMSA in the future.
On the physics side:
- The 2021 Physics Nobel Prize will be announced tomorrow morning. I gave up predicting these things after this prediction back in 2004.
- Gian Giudice has put on the arXiv a written version of his Theory closing talk at LCHP2021. He ends with
These are interesting times for particle physics: times of great uncertainty, in which our physics perspective is changing, and in which we are laying the foundations for the future of our field. As a community, we must rise to the challenge.
What worries me is that the much of the rest of the article contains a lot of
- Arguing for multiverse pseudo-science:
The multiverse describes a physical reality that challenges the presumption that there must be a single unified theory in the deep UV. In a sense, it is the ultimate Copernican revolution since not even the patch of the universe we live in is special. It implies a revision of the cosmological principle because the universe is approximately homogeneous and isotropic only within our horizon, but may be globally highly non-homogeneous. The multiverse is not an abstract idea, but it is a generic consequence of a large class of inflationary theories, where unavoidable quantum fluctuations of the inflaton spark a chain process with eternal creation of regions that expand faster than the surrounding space.
The multiverse is actually a familiar instrument of our everyday physics toolkit.
- Arguing against the fundamental significance of symmetry principles:
There are also theoretical indications for questioning the concept of symmetry. It is nowbelieved (and to a certain extent proven) that any global symmetry is violated at the level of quantum gravity. This means that any global symmetry that we observe in nature is only an accidental effect of looking at a system without sufficient short-distance resolution. The case of gauge symmetries is more subtle. Gauge symmetries are not real physical symmetries, in the sense
that they don’t correspond to an invariance under a physical transformation, but only to a redundancy of the coordinate parametrisation. We often confuse our students on this point by showing them the Mexican-hat potential and leading them to believe that there is a degeneracy of vacua, when in reality there is only one single vacuum state that breaks EW symmetry, as it is clear from the fact that the physical spectrum doesn’t contain any Goldstone boson corresponding to zero-energy excitations. Gauge symmetries may not be as fundamental as we thought, but only an emergent phenomenon. They could be a mirage of a different reality that takes place at a more fundamental level.
It’s looking depressingly possible that leaders of the field will push through as new “foundations for the future of our field” the argument that “the multiverse did it and symmetry is a mirage.” Instead of moving forward, the field will take a huge step backwards.
I spent yesterday up in Providence, visiting the Theoretical Physics Center at Brown, and giving a talk there (slides are available here, newer version of a paper here), At some point a recording of the talk should appear online. In the talk I tried to emphasize some basic things which it took me a very long time to appreciate:
- The ways in which Euclidean QFT is very different than Minkowski space-time QFT, in particular the necessity of having a distinguished imaginary time vector, breaking SO(4) invariance, in order to recover Lorentz (SL(2,C)) invariance.
- The way in which Minkowski space-time shows up when you do twistor theory in Euclidean space-time (see the pictures in the slides). This again makes clear the way SO(4) invariance is broken.
While I’m making a proposal for how to get gravity out of chiral 4d geometry, I’ve never been that expert in GR, and GR is the focus of much of the theory community these days, in particular the theorists at Brown. So, they had lots of questions about what the implications of this are for GR that I couldn’t answer. I’ll keep thinking more about this and may some day start to have answers (or maybe GR experts will find this proposal interesting enough to figure out the answers themselves).
I was invited to give the talk by Stephon Alexander, and got to spend some time talking with him while in Providence. He has worked in the past (see here) on ideas that bring together the gravitational and weak interactions in a similar way. More recently he has been working on ideas for how one might observe an unexpected chiral component to the gravitational interactions, and now has a grant from the Simons Foundation that will fund work in this area. Next week he’ll be here at Columbia giving an astronomy colloquium on the topic.
He also has a new book (his first was The Jazz of Physics) out, Fear of a Black Universe: an Outsider’s Guide to the Future of Physics. It’s quite interesting, with much of the earlier parts describing some of his experiences making a career for himself as a theorist, together with explanations of the physics background. The last part (in collaboration with Jaron Lanier) heads off in somewhat of a sci-fi direction, an excerpt is here.
A major theme of the book (with which I’m very sympathetic) is that the community doing this sort of theoretical physics desperately needs to get out of its current rut and open itself to new ideas, which often will come from “outsiders”. One aspect of being an “outsider” that Alexander has experienced is difference in racial background, but he’s concerned with a more general context of hostility to ideas that aren’t those currently favored by “insiders”. While he started out his career doing string theory, he has moved in different directions over the years. He explains that as a postdoc at SLAC he invited Lee Smolin to come and lecture on loop quantum gravity, something which was not at all well received by the local string theorists. While I’m quite interested for my own reasons to understand better what he has been doing with the physics of possible chiral effects in gravity, it was great to see his enthusiasm for and encouragement of ideas that don’t fit exactly into the narrow conception of the subject that now dominates all too much of the community doing fundamental theoretical physics.
Update: There’s video of the talk available here.
I’ve completely re-organized and largely rewritten my paper from earlier this year on Euclidean Spinors and Twistor Unification. Soon I’ll upload this as a revision to the arXiv, for now it’s available here. This new version starts from a very basic point of view about 4d geometry, leaving the technicalities about Euclidean QFT for spinors and the expository material about twistors to appendices.
Most ideas I’ve worked on over the years that seemed initially promising ultimately became more and more problematic the more I looked at them. This set of ideas keeps looking more and more solid. There are several (to me at least…) attractive aspects:
- Spinors are tautological objects (a point in space-time is a space of Weyl spinors), rather than complicated objects that must be separately introduced in the usual geometrical formalism.
- Analytic continuation between Minkowski and Euclidean space-time can be naturally performed, since twistor geometry provides their joint complexification.
- Exactly the internal symmetries of the Standard Model occur.
- The intricate transformation properties of a generation of Standard Model fermions correspond to a simple construction.
- One gets a new chiral formulation of gravity, unified with the Standard Model.
- Conformal symmetry is built into the picture in a fundamental way.
There’s more in this version about how quantum gravity fits into this, when formulated in terms of chiral variables (i.e. Ashtekar variables). This gives a new context for old questions about quantizing in these variables (this is in Eucldean signature, the other chirality is not space-time geometry but internal Yang-Mills geometry, and the imaginary time component of the vierbein is distinguished and given the dynamics of a Higgs field). I haven’t spent much time on this yet, but suspect this new context may help overcome problems that people trying to pursue quantum gravity in this chiral connection framework have run into in the past.
One common reaction I’ve gotten to these ideas is the one I myself had in the past: analytic continuation relates expectation values of field operators in Euclidean and Minkowski signature, so my left-handed SU(2) after analytic continuation gives part of Lorentz symmetry, not an internal symmetry. What took me a long time to realize is just how different Euclidean and Minkowski signature QFT is. Yes, Schwinger functions and Wightman functions can be related by analytic continuation (in a rather subtle way, the Wightman functions aren’t functions, but boundary values of holomorphic functions). But at the level of states and operators things are very different. It’s just not true that there is some holomorphic formulation of QFT states and operators, with Euclidean and Minkowski space restrictions related by analytic continuation. There’s a lot of explanation about this in the paper.
One objection I’ve run into is that by distinguishing a direction in Euclidean space I’m breaking Lorentz symmetry. What’s true is quite the opposite: having such a distinguished direction is needed to get Lorentz symmetry after analytic continuation. If you want to start in Euclidean space and get Lorentz symmetry, you have to do something like distinguish a direction and get an Osterwalder-Schrader reflection in that direction, which you need to get from SO(4) to SL(2,C). From the other direction, if you start in Minkowski space-time and analytically continue, you have a choice of lots of possible Euclidean slices to analytically continue to. You need to pick one, and that will distinguish an imaginary time direction. This is most easily seen in the twistor formalism, where the Minkowski space-time geometry is determined by a quadratic form that picks out a 5-dimensional hypersurface in PT. This will project down to an imaginary time = 0 subspace of Euclidean space-time, which picks out the imaginary time direction.
Today Quanta has One Lab’s Quest to Build Space-Time Out of Quantum Particles. No, this kind of experiment is not going to “Build Space-Time”, now or ever. This kind of obfuscation about quantum gravity advances neither fundamental physics nor the public understanding of it, quite the opposite. The article does make clear what the motivation is: deal with the problem that
String theory, still the leading candidate to replace the Standard Model, has often been accused of being untestable.
by claiming that it somehow can be tested in a lab.